💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Get the answer to your homework problem.

Try Numerade Free for 7 Days

Like

Report

Express the number as a ratio of intergers.$ 0. \overline 8 = 0.8888 . . . $

$$\frac{8}{9}$$

Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 2

Series

Sequences

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Boston College

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

01:06

Express the number as a ra…

00:33

Write the ratio in two oth…

00:37

Write each ratio in simple…

00:03

Write each ratio as a frac…

00:19

Write an equivalent fracti…

00:16

00:36

00:13

Find the reciprocal of the…

01:01

Write the ratio in lowest …

00:26

Simplify the ratio.$$<…

it's expressed this given number as a ratio of two imagers. What that means is we'd like to write this given number this decimal in the form of peel Rick. You. We're peeing Q or numbers such as, like negative, too negative wine zero one two and so on. Positive or negative? No fractions, But people like you will be our fraction. So here the way to do this is to write this as a geometric. So that's right as a geometric, Siri's. So the way to do that here it is, too. Let me raise this and you come down here some just going to rewrite this. So this is point eight and then point Oh, eight point zero zero eight and so on. And then here I can write. This first term is eight over ten plus and that here it looks like we move the decimal one place of the left. So we just multiplied by another ten on the bottom. Same thing over here, another place to the left. So that's ten cubed and we could see the pattern there. Now we can see its geometric and for a geometric series Not that this comm urges and our problems. Cube's Our is the number that were multiplying by each time. What are we most applying to go from here to here? It's one over ten. So in particular we have. This is true, so we know it emerges and we know the sum for geometric is the first term of the Siri's, all divided by one minus R. Now, in our problem, the first term is it over there and then we divide by one minus. R and R is one over ten. Let's go to simplify that, that's eight over ten overnight over ten and then cancel those tens and Europe with end up with eight over nine. And we've completed the task because we started with a decimal, and then we wrote it as a ratio of two imagers a day and night. That's our final answer

In mathematics, integration is one of the two main operations in calculus, w…

In grammar, determiners are a class of words that are used in front of nouns…

Express the number as a ratio of integers.$0 . \overline{8}=0.8888 \ldot…

Write the ratio in two other ways.$$\frac{1}{8}$$

Write each ratio in simplest form.The ratio of 8 in. to $3 \mathrm{ft}$.…

Write each ratio as a fraction. See Example $1 .$5 to 8

Write an equivalent fraction with the given denominator.$$\frac{0}{8}$$<…

Write each ratio in simplest form.$12 : 8$

Write the ratio in two other ways.$$8: 13$$

Find the reciprocal of the number.$$-8$$

Write the ratio in lowest terms with whole numbers in the numerator and deno…

Simplify the ratio.$$\frac{6-(-4)}{8-3}$$